CA FOUNDATION: QUANTITATIVE APTITUDE · RATIO AND PROPORTION, INDICES, LOGARITHMS

Indices: fractional and negative powers

a^(m/n) = (ⁿ√a)^m and a^(−m) = 1 ÷ a^m. Take the root first, then the power.

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Worked examples

Example 1 · level 1

Evaluate 64^(3/2).

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64 = 8^2.
(8^2)^(3/2) = 8^(3).
8^3 = 512.

Answer: 512

Example 2 · level 2

Evaluate 64^(3/2).

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64 = 8^2.
(8^2)^(3/2) = 8^(3).
8^3 = 512.

Answer: 512

Example 3 · level 3

Evaluate 27^(−1/3). Give the answer as a fraction.

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27 = 3^3.
(3^3)^(−1/3) = 3^(−1).
3^(−1) = 1/3^1 = 1/3.

Answer: 1/3